Spatial Straight-Line Drawing Algorithm Based on Method of Discriminate Regions—A Control Algorithm of Motors

Wang, Jianping; Xiao, Shiguang; Tao, Song; Yue, Junqi; Bian, Pingyan; Li, Yu

doi:10.3390/en13195002

Cited by 2 publications

(3 citation statements)

References 24 publications

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“…To our knowledge, we found no papers using step interpolation of QSICs or reference pulse interpolation of QSICs with constant feedrate. Recently, [10] adds a fifth imperfect 3D-line IPO to the imperfect-3D-line IPOs of [1; 4, §3.2], it argues to be better than [8], because the "discriminant contains decimals". That is completely wrong, because the four referenced IPOs [1; 4, §3.2] are basic integer arithmetic algorithms, although most of them can be used with floating point arithmetic too.…”

Section: Introduction To the Intersection Curve Of Two Quadrics (Qsic)mentioning

confidence: 99%

Perfect 3D-curve RMDPL-IPOs& Bresenham’s 3D-Curve Algorithm (Part 2 & 3)

Huypens¹

2021

Preprint

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<div>The paper presents three new 26-connected constant feedrate incremental step algorithms that can be used in practical situations in CNC machining tools. The 1st, the perfect 3D line IPO is 100% incremental, the word "perfect" means that the accuracy can be much better than the accuracy of Bresenham's 3D line (e.g. accuracy can be 37% worse). The simplified state diagram computes one perfect major axis points and possibly a perfect non-major axis point. The selection criterion uses the real 3D distance to the line. The 2nd, the perfect 3D curve IPO is a QSIC-algorithm (intersection of two quadrics). The selection criterion uses the "Relative Curve Measurement Theorem" extended to quadrics and QSICs. The consequences of this theorem are crucial, it means that one must not calculate the time-consuming distance to the 3D curve, but it suffices to calculate the RMDPL or the relative minimal distance of two candidate points to the polar line of the QSIC with respect to the midpoint of the candidate points. As the midpoints are close to the curve, the polar lines enclose and inclose the curve. Theoretical, the RMDPL is fundamental, it is the core of all the successful 2D incremental step algorithms and the paper proves that it is the core of the 3D incremental step algorithms or the 3D reference pulse IPOs. Thanks to the RMDPL, the paper represents QSICs in a unique way comparable with 3D-lines. The 3rd, Bresenham's imperfect 3D curve IPO is less accurate but super-fast and can be used in many practical situations as the maximum error (MaxErr) is bounded to 0.707. The curve algorithms can have singular points, but that problem is simple solved. Each curve is a sub-segment of a monotonic curve from the starting extreme point to the ending extreme point. All the extreme points and the singular points are offline precomputed as the intersection points of three quadrics. The constant feedrate of sampled-data curves is clear when the arc length is known, but the real time calculation of the arc length of incremental step curves was until now an open problem. The former paper used the super-fast PRM-cs algorithm for 3D-lines and 2D curves and the same constant feedrate algorithm (actually, a real time length algorithm) can be used even in integer form. The implementation of the constant feedrate algorithm to a 26-connected curve with high accuracy turns out to be piece of cake in contrast to the sampled-data curves. All IPOs can be converted to constant feedrate listSIM-IPOs which can be used in real time in rigid simplified CNC machine tools.</div>

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Section: Introduction To the Intersection Curve Of Two Quadrics (Qsic)mentioning

confidence: 99%

Perfect 3D-curve RMDPL-IPOs& Bresenham’s 3D-Curve Algorithm (Part 2 & 3)

Huypens¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Recently, [10] adds a fifth imperfect 3D-line IPO to the imperfect-3D-line IPOs of [1; 2, § 3.2], it argues to be better than [8], because the "discriminant contains decimals". That is wrong, because the four referenced IPOs are basic integer arithmetic algorithms, although most of them can use decimal fixed-point arithmetic too.…”

mentioning

confidence: 99%

“…That is wrong, because the four referenced IPOs are basic integer arithmetic algorithms, although most of them can use decimal fixed-point arithmetic too. The algorithm [10,Fig. 5] [43] it is unsuitable to group the RMD interpolators as RMD interpolators.…”

mentioning

confidence: 99%

Relative Minimum Distance 3D-curve and 3D-Offsets Real Time Constant Feedrate Algorithms

Huypens¹

2022

Preprint

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<p>The constant feedrate 3D RMD algorithms avoid most of the constraints introduced by the sampled-data system (chord error, inaccuracy, jerk). The main bottlenecks were the computations of the intersections (QSICs) of the implicit quadrics, the determination of the candidate point with the minimum distance to the QSIC (the best incremental step), the small execution time per step and the fast determination of the small 3D-offsets.The Twopoint RMD IPO is the extension to implicit polynomials of degree higher than two.</p>

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Spatial Straight-Line Drawing Algorithm Based on Method of Discriminate Regions—A Control Algorithm of Motors

Cited by 2 publications

References 24 publications

Perfect 3D-curve RMDPL-IPOs& Bresenham’s 3D-Curve Algorithm (Part 2 & 3)

Perfect 3D-curve RMDPL-IPOs& Bresenham’s 3D-Curve Algorithm (Part 2 & 3)

Relative Minimum Distance 3D-curve and 3D-Offsets Real Time Constant Feedrate Algorithms

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